{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 一、数据分析和处理"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3327, 81) (1427, 81) (3327,) (1427,)\n",
      "0    1068\n",
      "1     359\n",
      "Name: status, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd \n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "df = pd.read_csv('data.csv',encoding = 'gbk')\n",
    "\n",
    "\"\"\"\n",
    "数据处理\n",
    "\"\"\"\n",
    "\n",
    "###删除无关特征###\n",
    "df.drop(['Unnamed: 0','custid','trade_no','bank_card_no' ,'source','id_name'],inplace =True,axis = 1)\n",
    "\n",
    "###数据类型转换###（主要针对 obeject（文字类） \n",
    "df['reg_preference_for_trad'].fillna('其他城市',inplace = True)\n",
    "df['reg_preference_for_trad'].replace({'一线城市':1,'二线城市':2,'三线城市':3,'境外':4,'其他城市':5},inplace = True)\n",
    "\n",
    "# 处理日期格式 'latest_query_time', 'loans_latest_time'(暂时去掉？？？)\n",
    "\n",
    "df.drop(['latest_query_time', 'loans_latest_time'],inplace =True,axis = 1)\n",
    "\n",
    "\n",
    "###缺失值处理###\n",
    "df['student_feature'].fillna(0,inplace=True) \n",
    "for i in df.columns:\n",
    "    df[i].fillna(df[i].mode()[0],inplace = True)  #加[0]是因为众数可能有多个，返回不是一个数字\n",
    "    \n",
    "###切分数据集###\n",
    "\n",
    "y=df['status']\n",
    "x=df.drop('status',axis=1)\n",
    "x_train,x_test,y_train,y_test =train_test_split(x,y,test_size=0.3,random_state = 2018)   \n",
    "print(x_train.shape, x_test.shape, y_train.shape, y_test.shape)\n",
    "print(y_test.value_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 二、特征选择"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## 三、建模"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.svm import LinearSVC\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import BaggingClassifier, RandomForestClassifier, AdaBoostClassifier, GradientBoostingClassifier\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.linear_model import Perceptron\n",
    "import xgboost as xgb\n",
    "import lightgbm as lgb\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from pandas import DataFrame,Series\n",
    "\n",
    "### 标准化处理 ### 必须要做的\n",
    "features = x_train.columns #目前是83个特征\n",
    "scaler = StandardScaler()\n",
    "x_train = scaler.fit_transform(x_train)\n",
    "x_test = scaler.fit_transform(x_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 模型"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.基本的分类器 ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Perceptron(alpha=0.0001, class_weight=None, eta0=1.0, fit_intercept=True,\n",
       "      max_iter=50, n_iter=None, n_jobs=1, penalty=None, random_state=0,\n",
       "      shuffle=True, tol=None, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#感知机\n",
    "clf_pt = Perceptron(max_iter=50)\n",
    "clf_pt.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#逻辑回归\n",
    "clf_lr = LogisticRegression()\n",
    "clf_lr.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearSVC(C=1, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='hinge', max_iter=1000, multi_class='ovr',\n",
       "     penalty='l2', random_state=None, tol=0.0001, verbose=0)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#svm\n",
    "clf_svm = LinearSVC(C=1, loss=\"hinge\")\n",
    "clf_svm.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
       "            max_features=None, max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, presort=False, random_state=None,\n",
       "            splitter='best')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#决策树\n",
    "clf_dt = DecisionTreeClassifier()\n",
    "clf_dt.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianNB(priors=None)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 高斯朴素贝叶斯\n",
    "clf_gnb = GaussianNB()\n",
    "clf_gnb.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.基于sklearn的集成学习 ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',\n",
       "            max_depth=None, max_features='auto', max_leaf_nodes=None,\n",
       "            min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "            min_samples_leaf=1, min_samples_split=2,\n",
       "            min_weight_fraction_leaf=0.0, n_estimators=10, n_jobs=-1,\n",
       "            oob_score=False, random_state=2018, verbose=0,\n",
       "            warm_start=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#随机森林\n",
    "clf_rf = RandomForestClassifier(random_state=2018, n_jobs=-1)\n",
    "clf_rf.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GradientBoostingClassifier(criterion='friedman_mse', init=None,\n",
       "              learning_rate=0.1, loss='deviance', max_depth=3,\n",
       "              max_features=None, max_leaf_nodes=None,\n",
       "              min_impurity_decrease=0.0, min_impurity_split=None,\n",
       "              min_samples_leaf=1, min_samples_split=2,\n",
       "              min_weight_fraction_leaf=0.0, n_estimators=100,\n",
       "              presort='auto', random_state=None, subsample=1.0, verbose=0,\n",
       "              warm_start=False)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# GBDT\n",
    "clf_gbdt = GradientBoostingClassifier()\n",
    "clf_gbdt.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:   38.0s finished\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "BaggingClassifier(base_estimator=LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
       "     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
       "     verbose=0),\n",
       "         bootstrap=True, bootstrap_features=False, max_features=1.0,\n",
       "         max_samples=1.0, n_estimators=60, n_jobs=1, oob_score=False,\n",
       "         random_state=2018, verbose=1, warm_start=False)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Bagging 这个耗时长\n",
    "clf_bg = BaggingClassifier(base_estimator=LinearSVC(), n_estimators=60, max_samples=1.0, max_features=1.0, random_state=2018,\n",
    "                        n_jobs=1, verbose=1)\n",
    "clf_bg.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "AdaBoostClassifier(algorithm='SAMME',\n",
       "          base_estimator=LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
       "     intercept_scaling=1, loss='squared_hinge', max_iter=1000,\n",
       "     multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
       "     verbose=0),\n",
       "          learning_rate=1.0, n_estimators=50, random_state=None)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Adaboost\n",
    "clf_ab = AdaBoostClassifier(base_estimator=LinearSVC(), n_estimators=50,algorithm='SAMME')\n",
    "clf_ab.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.大杀器 ###"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "XGBClassifier(base_score=0.5, booster='gbtree', colsample_bylevel=1,\n",
       "       colsample_bytree=1, gamma=0.1, learning_rate=0.1, max_delta_step=0,\n",
       "       max_depth=6, min_child_weight=3, missing=None, n_estimators=100,\n",
       "       n_jobs=1, nthread=32, num_class=2, objective='multi:softmax',\n",
       "       random_state=0, reg_alpha=0, reg_lambda=1, scale_pos_weight=1,\n",
       "       seed=1000, silent=True, subsample=1)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#xgb\n",
    "clf_xgb = xgb.XGBClassifier(max_depth=6, num_class =2,learning_rate=0.1, n_estimators=100, silent=True, objective='multi:softmax',\n",
    "                        nthread=32, gamma=0.1, min_child_weight=3, max_delta_step=0, subsample=1, colsample_bytree=1,\n",
    "                        colsample_bylevel=1, reg_alpha=0, reg_lambda=1, scale_pos_weight=1, base_score=0.5, seed=1000,\n",
    "                        missing=None)\n",
    "clf_xgb.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LGBMClassifier(boosting_type='gbdt', class_weight=None, colsample_bytree=1.0,\n",
       "        importance_type='split', learning_rate=0.1, max_bin=255,\n",
       "        max_depth=-1, min_child_samples=20, min_child_weight=0.001,\n",
       "        min_split_gain=0.0, n_estimators=250, n_jobs=-1, num_leaves=31,\n",
       "        objective=None, random_state=None, reg_alpha=0.0, reg_lambda=0.5,\n",
       "        silent=True, subsample=1.0, subsample_for_bin=200000,\n",
       "        subsample_freq=1)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# lgbm\n",
    "clf_lgbm = lgb.LGBMClassifier(boosting_type='gbdt', num_leaves=31, max_depth=-1, learning_rate=0.1, n_estimators=250,\n",
    "                              max_bin=255, subsample_for_bin=200000, objective=None, min_split_gain=0.0, min_child_weight=0.001,\n",
    "                              min_child_samples=20, subsample=1.0, subsample_freq=1, colsample_bytree=1.0, reg_alpha=0.0,\n",
    "                              reg_lambda=0.5, random_state=None, n_jobs=-1, silent=True)\n",
    "clf_lgbm.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.1s finished\n",
      "[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.0s finished\n"
     ]
    }
   ],
   "source": [
    "# 11个模型：\n",
    "##感知机,逻辑回归,svm,决策树,高斯朴素贝叶斯，随机森林，GBDT，Bagging ，Adaboost，xgb，lgbm\n",
    "\n",
    "#对train\n",
    "y_train_pt = clf_pt.predict(x_train)\n",
    "y_train_lr = clf_lr.predict(x_train)\n",
    "y_train_svm = clf_svm.predict(x_train)\n",
    "y_train_dt = clf_dt.predict(x_train)\n",
    "y_train_gnb = clf_gnb.predict(x_train)\n",
    "\n",
    "y_train_rf = clf_rf.predict(x_train)\n",
    "y_train_gbdt = clf_gbdt.predict(x_train)\n",
    "y_train_bg = clf_bg.predict(x_train)\n",
    "y_train_ab = clf_ab.predict(x_train)\n",
    "\n",
    "y_train_xgb = clf_xgb.predict(x_train)\n",
    "y_train_lgbm = clf_lgbm.predict(x_train)\n",
    "\n",
    "#对test\n",
    "y_test_pt = clf_pt.predict(x_test)\n",
    "y_test_lr = clf_lr.predict(x_test)\n",
    "y_test_svm = clf_svm.predict(x_test)\n",
    "y_test_dt = clf_dt.predict(x_test)\n",
    "y_test_gnb = clf_gnb.predict(x_test)\n",
    "\n",
    "y_test_rf = clf_rf.predict(x_test)\n",
    "y_test_gbdt = clf_gbdt.predict(x_test)\n",
    "y_test_bg = clf_bg.predict(x_test)\n",
    "y_test_ab = clf_ab.predict(x_test)\n",
    "\n",
    "y_test_xgb = clf_xgb.predict(x_test)\n",
    "y_test_lgbm = clf_lgbm.predict(x_test)\n",
    "\n",
    "#交叉验证\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 四、模型评估"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 混淆矩阵\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "from sklearn.metrics import confusion_matrix, precision_score, accuracy_score,recall_score, f1_score,roc_auc_score\n",
    "\n",
    "def get_eval(y_train,y_test,y_train_pred,y_test_pred,model_name):\n",
    "    train_dataList = []\n",
    "    test_dataList = []\n",
    "    print('for model {}:'.format(str(model_name)))\n",
    "    train_dataList.append(str(model_name))\n",
    "    test_dataList.append(str(model_name))\n",
    "    train_dataList.append(str('train'))\n",
    "    test_dataList.append(str('test'))\n",
    "\n",
    "#   混淆矩阵\n",
    "    obj1 = confusion_matrix(y_train, y_train_pred)\n",
    "    print('train_confusion_matrix\\n', obj1)\n",
    "    obj2 = confusion_matrix(y_test, y_test_pred)\n",
    "    print('test_confusion_matrix\\n', obj2)\n",
    "    \n",
    "#     print('accuracy:\\n')\n",
    "#     print('train:{}\\n test:{}\\n'.format(accuracy_score(y_train,y_train_pred),accuracy_score(y_test,y_test_pred)))\n",
    "    train_dataList.append(accuracy_score(y_train,y_train_pred))\n",
    "    test_dataList.append(accuracy_score(y_test,y_test_pred))\n",
    "#     print('precision:\\n')\n",
    "#     print('train:{}\\n test:{}\\n'.format(precision_score(y_train,y_train_pred),precision_score(y_test,y_test_pred)))\n",
    "    train_dataList.append(precision_score(y_train,y_train_pred))\n",
    "    test_dataList.append(precision_score(y_test,y_test_pred))\n",
    "#     print('recall:\\n')\n",
    "#     print('train:{}\\n test:{}\\n'.format(recall_score(y_train,y_train_pred),recall_score(y_test,y_test_pred)))\n",
    "    train_dataList.append(recall_score(y_train,y_train_pred))\n",
    "    test_dataList.append(recall_score(y_test,y_test_pred))\n",
    "#     print('f1-score:\\n')\n",
    "#     print('train:{}\\n test:{}\\n'.format(f1_score(y_train,y_train_pred),f1_score(y_test,y_test_pred)))\n",
    "    train_dataList.append(f1_score(y_train,y_train_pred))\n",
    "    test_dataList.append(f1_score(y_test,y_test_pred))\n",
    "#     print('AUC:\\n')\n",
    "#     print('train:{}\\n test:{}\\n'.format(roc_auc_score(y_train,y_train_pred),roc_auc_score(y_test,y_test_pred)))\n",
    "    train_dataList.append(roc_auc_score(y_train,y_train_pred))\n",
    "    test_dataList.append(roc_auc_score(y_test,y_test_pred))\n",
    "    return train_dataList,test_dataList"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "for model 感知机:\n",
      "train_confusion_matrix\n",
      " [[2131  362]\n",
      " [ 472  362]]\n",
      "test_confusion_matrix\n",
      " [[874 194]\n",
      " [212 147]]\n",
      "for model 逻辑回归:\n",
      "train_confusion_matrix\n",
      " [[2361  132]\n",
      " [ 519  315]]\n",
      "test_confusion_matrix\n",
      " [[998  70]\n",
      " [234 125]]\n",
      "for model SVM:\n",
      "train_confusion_matrix\n",
      " [[2423   70]\n",
      " [ 580  254]]\n",
      "test_confusion_matrix\n",
      " [[1022   46]\n",
      " [ 275   84]]\n",
      "for model 决策树:\n",
      "train_confusion_matrix\n",
      " [[2493    0]\n",
      " [   0  834]]\n",
      "test_confusion_matrix\n",
      " [[826 242]\n",
      " [211 148]]\n",
      "for model 高斯朴素贝叶斯:\n",
      "train_confusion_matrix\n",
      " [[1401 1092]\n",
      " [ 196  638]]\n",
      "test_confusion_matrix\n",
      " [[952 116]\n",
      " [264  95]]\n",
      "for model 随机森林:\n",
      "train_confusion_matrix\n",
      " [[2493    0]\n",
      " [  50  784]]\n",
      "test_confusion_matrix\n",
      " [[992  76]\n",
      " [278  81]]\n",
      "for model GBDT:\n",
      "train_confusion_matrix\n",
      " [[2432   61]\n",
      " [ 405  429]]\n",
      "test_confusion_matrix\n",
      " [[1004   64]\n",
      " [ 258  101]]\n",
      "for model Bagging:\n",
      "train_confusion_matrix\n",
      " [[2385  108]\n",
      " [ 541  293]]\n",
      "test_confusion_matrix\n",
      " [[1006   62]\n",
      " [ 248  111]]\n",
      "for model AdaBoosting:\n",
      "train_confusion_matrix\n",
      " [[2383  110]\n",
      " [ 543  291]]\n",
      "test_confusion_matrix\n",
      " [[1005   63]\n",
      " [ 249  110]]\n",
      "for model XGBoosting:\n",
      "train_confusion_matrix\n",
      " [[2492    1]\n",
      " [  41  793]]\n",
      "test_confusion_matrix\n",
      " [[1008   60]\n",
      " [ 261   98]]\n",
      "for model lightGBM:\n",
      "train_confusion_matrix\n",
      " [[2493    0]\n",
      " [   0  834]]\n",
      "test_confusion_matrix\n",
      " [[989  79]\n",
      " [252 107]]\n"
     ]
    }
   ],
   "source": [
    "all_dataList = []\n",
    "index = []\n",
    "a1,a2 = get_eval(y_train,y_test,y_train_pt,y_test_pt,'感知机')\n",
    "b1,b2 = get_eval(y_train,y_test,y_train_lr,y_test_lr,'逻辑回归')\n",
    "c1,c2 = get_eval(y_train,y_test,y_train_svm,y_test_svm,'SVM')\n",
    "d1,d2 = get_eval(y_train,y_test,y_train_dt,y_test_dt,'决策树')\n",
    "e1,e2 = get_eval(y_train,y_test,y_train_gnb,y_test_gnb,'高斯朴素贝叶斯')\n",
    "f1,f2 = get_eval(y_train,y_test,y_train_rf,y_test_rf,'随机森林')\n",
    "g1,g2 = get_eval(y_train,y_test,y_train_gbdt,y_test_gbdt,'GBDT')\n",
    "h1,h2 = get_eval(y_train,y_test,y_train_bg,y_test_bg,'Bagging')\n",
    "i1,i2 = get_eval(y_train,y_test,y_train_ab,y_test_ab,'AdaBoosting')\n",
    "j1,j2 = get_eval(y_train,y_test,y_train_xgb,y_test_xgb,'XGBoosting')\n",
    "k1,k2 = get_eval(y_train,y_test,y_train_lgbm,y_test_lgbm,'lightGBM')\n",
    "all_dataList = [a1,a2,b1,b2,c1,c2,d1,d2,e1,e2,f1,f2,g1,g2,h1,h2,i1,i2,j1,j2,k1,k2]\n",
    "df_all = pd.DataFrame(all_dataList,columns=['model_name','dataset','accuracy','precision','recall','f1_score','AUC'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib notebook\n",
    "def plot_roc_curve(fpr,tpr,label = None):\n",
    "    plt.plot(fpr,tpr,linewidth = 2,label = label)\n",
    "    plt.plot([0,1],[0,1],'k--')\n",
    "    plt.axis([0,1,0,1])\n",
    "    plt.xlabel = ('False Positive Rate')\n",
    "    plt.ylabel = ('True Positive Rate')\n",
    "    plt.show()\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>model_name</th>\n",
       "      <th>dataset</th>\n",
       "      <th>accuracy</th>\n",
       "      <th>precision</th>\n",
       "      <th>recall</th>\n",
       "      <th>f1_score</th>\n",
       "      <th>AUC</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>感知机</td>\n",
       "      <td>train</td>\n",
       "      <td>0.749324</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.434053</td>\n",
       "      <td>0.464698</td>\n",
       "      <td>0.644423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>感知机</td>\n",
       "      <td>test</td>\n",
       "      <td>0.715487</td>\n",
       "      <td>0.431085</td>\n",
       "      <td>0.409471</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.613911</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>逻辑回归</td>\n",
       "      <td>train</td>\n",
       "      <td>0.804328</td>\n",
       "      <td>0.704698</td>\n",
       "      <td>0.377698</td>\n",
       "      <td>0.491803</td>\n",
       "      <td>0.662375</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>逻辑回归</td>\n",
       "      <td>test</td>\n",
       "      <td>0.786966</td>\n",
       "      <td>0.641026</td>\n",
       "      <td>0.348189</td>\n",
       "      <td>0.451264</td>\n",
       "      <td>0.641323</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>SVM</td>\n",
       "      <td>train</td>\n",
       "      <td>0.804629</td>\n",
       "      <td>0.783951</td>\n",
       "      <td>0.304556</td>\n",
       "      <td>0.438687</td>\n",
       "      <td>0.638239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>SVM</td>\n",
       "      <td>test</td>\n",
       "      <td>0.775053</td>\n",
       "      <td>0.646154</td>\n",
       "      <td>0.233983</td>\n",
       "      <td>0.343558</td>\n",
       "      <td>0.595456</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>决策树</td>\n",
       "      <td>train</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>决策树</td>\n",
       "      <td>test</td>\n",
       "      <td>0.682551</td>\n",
       "      <td>0.379487</td>\n",
       "      <td>0.412256</td>\n",
       "      <td>0.395194</td>\n",
       "      <td>0.592832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>高斯朴素贝叶斯</td>\n",
       "      <td>train</td>\n",
       "      <td>0.612864</td>\n",
       "      <td>0.368786</td>\n",
       "      <td>0.764988</td>\n",
       "      <td>0.497660</td>\n",
       "      <td>0.663481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>高斯朴素贝叶斯</td>\n",
       "      <td>test</td>\n",
       "      <td>0.733707</td>\n",
       "      <td>0.450237</td>\n",
       "      <td>0.264624</td>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.578005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>随机森林</td>\n",
       "      <td>train</td>\n",
       "      <td>0.984971</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.940048</td>\n",
       "      <td>0.969098</td>\n",
       "      <td>0.970024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>随机森林</td>\n",
       "      <td>test</td>\n",
       "      <td>0.751927</td>\n",
       "      <td>0.515924</td>\n",
       "      <td>0.225627</td>\n",
       "      <td>0.313953</td>\n",
       "      <td>0.577233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>GBDT</td>\n",
       "      <td>train</td>\n",
       "      <td>0.859934</td>\n",
       "      <td>0.875510</td>\n",
       "      <td>0.514388</td>\n",
       "      <td>0.648036</td>\n",
       "      <td>0.744960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GBDT</td>\n",
       "      <td>test</td>\n",
       "      <td>0.774352</td>\n",
       "      <td>0.612121</td>\n",
       "      <td>0.281337</td>\n",
       "      <td>0.385496</td>\n",
       "      <td>0.610706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Bagging</td>\n",
       "      <td>train</td>\n",
       "      <td>0.804929</td>\n",
       "      <td>0.730673</td>\n",
       "      <td>0.351319</td>\n",
       "      <td>0.474494</td>\n",
       "      <td>0.653999</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Bagging</td>\n",
       "      <td>test</td>\n",
       "      <td>0.782761</td>\n",
       "      <td>0.641618</td>\n",
       "      <td>0.309192</td>\n",
       "      <td>0.417293</td>\n",
       "      <td>0.625570</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>AdaBoosting</td>\n",
       "      <td>train</td>\n",
       "      <td>0.803727</td>\n",
       "      <td>0.725686</td>\n",
       "      <td>0.348921</td>\n",
       "      <td>0.471255</td>\n",
       "      <td>0.652399</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>AdaBoosting</td>\n",
       "      <td>test</td>\n",
       "      <td>0.781359</td>\n",
       "      <td>0.635838</td>\n",
       "      <td>0.306407</td>\n",
       "      <td>0.413534</td>\n",
       "      <td>0.623709</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>XGBoosting</td>\n",
       "      <td>train</td>\n",
       "      <td>0.987376</td>\n",
       "      <td>0.998741</td>\n",
       "      <td>0.950839</td>\n",
       "      <td>0.974201</td>\n",
       "      <td>0.975219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>XGBoosting</td>\n",
       "      <td>test</td>\n",
       "      <td>0.775053</td>\n",
       "      <td>0.620253</td>\n",
       "      <td>0.272981</td>\n",
       "      <td>0.379110</td>\n",
       "      <td>0.608400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>lightGBM</td>\n",
       "      <td>train</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>lightGBM</td>\n",
       "      <td>test</td>\n",
       "      <td>0.768045</td>\n",
       "      <td>0.575269</td>\n",
       "      <td>0.298050</td>\n",
       "      <td>0.392661</td>\n",
       "      <td>0.612040</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     model_name dataset  accuracy  precision    recall  f1_score       AUC\n",
       "0           感知机   train  0.749324   0.500000  0.434053  0.464698  0.644423\n",
       "1           感知机    test  0.715487   0.431085  0.409471  0.420000  0.613911\n",
       "2          逻辑回归   train  0.804328   0.704698  0.377698  0.491803  0.662375\n",
       "3          逻辑回归    test  0.786966   0.641026  0.348189  0.451264  0.641323\n",
       "4           SVM   train  0.804629   0.783951  0.304556  0.438687  0.638239\n",
       "5           SVM    test  0.775053   0.646154  0.233983  0.343558  0.595456\n",
       "6           决策树   train  1.000000   1.000000  1.000000  1.000000  1.000000\n",
       "7           决策树    test  0.682551   0.379487  0.412256  0.395194  0.592832\n",
       "8       高斯朴素贝叶斯   train  0.612864   0.368786  0.764988  0.497660  0.663481\n",
       "9       高斯朴素贝叶斯    test  0.733707   0.450237  0.264624  0.333333  0.578005\n",
       "10         随机森林   train  0.984971   1.000000  0.940048  0.969098  0.970024\n",
       "11         随机森林    test  0.751927   0.515924  0.225627  0.313953  0.577233\n",
       "12         GBDT   train  0.859934   0.875510  0.514388  0.648036  0.744960\n",
       "13         GBDT    test  0.774352   0.612121  0.281337  0.385496  0.610706\n",
       "14      Bagging   train  0.804929   0.730673  0.351319  0.474494  0.653999\n",
       "15      Bagging    test  0.782761   0.641618  0.309192  0.417293  0.625570\n",
       "16  AdaBoosting   train  0.803727   0.725686  0.348921  0.471255  0.652399\n",
       "17  AdaBoosting    test  0.781359   0.635838  0.306407  0.413534  0.623709\n",
       "18   XGBoosting   train  0.987376   0.998741  0.950839  0.974201  0.975219\n",
       "19   XGBoosting    test  0.775053   0.620253  0.272981  0.379110  0.608400\n",
       "20     lightGBM   train  1.000000   1.000000  1.000000  1.000000  1.000000\n",
       "21     lightGBM    test  0.768045   0.575269  0.298050  0.392661  0.612040"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 同时看train和test可以知道有没有过拟合\n",
    "df_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 画ROC曲线\n",
    "from sklearn.metrics import roc_curve\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "def draw_roc(y_true, y_pred,label=None):\n",
    "    fpr, tpr, thresholds = roc_curve(y_true, y_pred)\n",
    "    plt.plot(fpr, tpr, linewidth = 2, label=label)\n",
    "    plt.plot([0,1],[0,1], 'k--')\n",
    "    plt.axis([0,1.1,0,1.1])\n",
    "    plt.xlabel('False Postivie Rate')\n",
    "    plt.ylabel('True Positive Rate')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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vXj5q9CQ6seZ26+oH/YzZx41Kztj+yMhIfH19OXHiBDt27CAgIIDJkyfbOyxR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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fe804128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IQ72D8G9QPCicEQ8xs2B3FBRkGW2N2xvjBZ0eABd3Bz1BxdlsNqxWK25ubgwf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\nXCVJOJvDvJg4vtyRQGau0UX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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fedeba20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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wZV1Gdwvmrro3ecBLa/hjBfz+DiRbAoZrBEH3CdB0cLHC6qyZO3cuQ4cOxdfX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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fedf6240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qW+2r6z0BgUXszZdLCQkJ9O/fn4CAAIYNG8Y//vEPuyMp5fOyKwoXjTHJAMaY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\nly7x1Vdfcdddd7n1Z6BHClf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/L9Yv8s7AQKy2z9mZ5VzvFBBrjDl/1es3lBPYjHU94T2g\no4hUBV4EGhtjTovIVCD4Gu8V4DtjTHcX9qMKID19pPxFKeC4c/KVJ7Gaq11BRG4HDjpPmczHOo2y\nHOgsImHOdcqIyG0u7nMfUEVE7nAuPwmscp6DL2WMWYJVrC7PlX0eKHGdba3Cmp6xD1edOnK6oZzO\nNtP/Au4TkbuAkkAycFasTqMRWVbPmmsj0PTyZxKR4iJyraMuVUBpUVD+4gOgl4hsx+q1n3yNdboA\nu0RkG1Aba7rDPVjn0L8VkR3Ad1inVnJkjEnF6l75lbODpwOYiPULdpFze2v53zn5WcBLzgvT1a7a\nVgbWaaYIrnG6KTc5jTEXgHewrmNsB7YCPwMzgHVZVo0BlorICmPMCeApYKZzPxuwfp5KAdolVSml\nVBZ6pKCUUiqTFgWllFKZtCgopZTKpEVBKaVUJi0KSimlMmlRUEoplUmLglJKqUxaFJRSSmX6f/c+\nsSTSCmz7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fee1e240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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F/d/B5k8h7pqxrUYnePx9qNAUs9nMy2PGMHv2bLTW1K5d2361FiDSFIQowrTWnLh2M32+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\n/f3Zv38/jo6O6QF2rq6uNrmeEKLosuW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FtmcCq4HbxrH+5UClKNi+xfZ9o61ge6Htf49x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\niKIQQgihIopCCCGEiigKIYQQKv4LvNVKLGjuSE8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fee1e3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pgJ1SDq40heeAl4A3HNNLgaEeq0jlTInxsGo4LB/iFFjXGe59B4qU80oJP/30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\ndSstW7YkJiaGnTt3Mnr0aLp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fed20be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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KOxbC6lcg97gxFtIVRsyE6Mng5ZzFdNu3b2fcuHF07tyZNWvWOOU9hPups8Vr\nWuuNti/PAL+3vXjbSytPNCZaa3an5tnOCMwcTK9oL9HMz5trehirikd2C6OZJ7aXqClLKWz/BNa8\nCrknjLHQy2H4TIi+0WlhYLVamT59Oh988AFaawYOHOiU9xGercr/ByqlBgJtgbVa60ylVBTwZ+Aa\noF091Cc8lNWq2Z6SY+88ejy7or1EcBNfrusRQWy0iaFdQz23vURNWUpg28ew5jXISzHGwrob00RR\nNzgtDADWrl1LXFwc2dnZBAUF8fnnnzN27FinvZ/wXFWtaP4vMBnYgXFxeSnwAPACcF/9lCc8SblV\n8+uRbJYnG0FgzqtY3hIa6MeYKGNnsis7heDrbpvWO1NZsREGa1+DvJPGWFgPY5qo5/Xg5fy/i1On\nTnH69GluvfVWPv74Y2lgJy6qqn8ZccAVWusipVQr4ATQS2t9uH5KE56g1GLll8NZJCal8n1yGlkF\npfbn2gQHMNa2V3H/9i09v71ETZUVw9YPYe3rcOaUMRYeZYRBj0lOD4NvvvmGt956i8TERG655RZG\njhxJeHi4U99TeL6qQqFYa10EoLXOVkrtl0AQYLSXWL0/g0Rbe4m84opN6zuENCUmujUx0SauaBfc\ncFYV10RZEWz5ENa9DmdSjbGIaBjxZ+g+welhkJ+fz/XXX89PP/10TgM7CQThiKpCoZNS6mwnVIWx\nP7O9M6rW+kanVibcSn6JhRV700lMNrNibzqFldpLdItobjsjMNHd1LxxBgEYYbD5fSMM8tOMMVMv\nIwy6ja+XaaKPPvqIe++9l+LiYiIjI/nuu++kgZ2okapCYfJ5j+c4sxDhfnILy/hxj7GqePWBDEor\ntZfo1TaYGFsQdAq7tA3fPV5pIWyeD+tmQ0G6MWbqDSOfgm7joJ5CMj09nTvuuAOlFE8//TTPP/98\nvbyvaFiqaoj3U30WItxDZn4J3yenkZCUyi+HsrDYlhUrBQPat7SvKr6sVQNsL1FTpQWw6T1Y/wYU\nZBhjrfsYYXB5TL2FwYIFC5gyZQrh4eHMnj2bSZMm0b59+3p5b9HwyC0IgtTcIvsags1HK9pLeHsp\nhnQJISbKCILwoAbaXqKmSvJh07uw/k0ozDTG2vQzwqDrmHoLg5SUFGJiYkhOTmbVqlXEx8fz8MMP\n18t7i4ZLQqGROpZVYN+0fvuJc9tLjOgSSmx0a67rGUGrZnXbltmjleTDpnm2MMgyxtr2h5F/gS7X\n1VsYADxY0zVtAAAgAElEQVT77LP8+9//pry8nP79+/Pcc8/V23uLhs3hUFBK+WutS6o/UrirA2nG\npvUJSWb2pFa0lwjw9WLk5eHE9jI2rQ8KaODtJWqq5Az8Gg/r50BRtjHWbiCMeAq6XFuvYQAwePBg\nfv31V/z9/XnnnXe4++676/X9RcNWbSgopQYB72H0PIpUSl0BTNday3mqm9Nak3wqj4SkVBKTzBzK\nKLA/F+jvw7U9womNNjatb+onJ42/UZwHv74Dv/wPik4bY5cNNu4m6nxNvYaB1WrFYrHg5+fH9ddf\nT0BAAN9++600sBN1zpGGeBuAKcDXWuu+trEkrXV0PdT3G9IQr2pWq2bbidMk7DKTmGwm5XSR/bkW\nTX0Z3SOC2F4mhnQJxd+nkbSXqKniXNhoC4Ni29Ra5FVGGHQaWe9nBps3b2bixIl07tyZtWvX1ut7\ni4ajzhriAV5a62Pn3XtefrGDRf2zlFv59Ug2iclmliebScurmOULa+7P2KgIYqNbM7hjK3waU3uJ\nmirKgY1zYcNbRjAAtB9ihEHH4fUeBlarlTvuuIOPP/4YgCuvvLJe3180To6EwgnbFJJWSnkDDwP7\nnVuWqE6pxcq6Q5kk7jLzw540siu1l2jbool9DUG/yJYNY9N6ZyrKgQ1vG/+VnA2DocbdRB2HuaSk\n1atXExcXR05ODi1atOCLL77g2muvdUktonFxJBTuB94AIoE04EfbWLWUUjHAbMAbeFdrPesCx4wE\nXgd8gUyt9QiHKm+EikrLWbU/g8SkVH7ak86Zkor2Ep1CmxFj26u4V9tG2l6ipgqzjSDYOBdKbBfe\nOwwzwqDDUJeWlpGRQW5uLrfddhsffPCBNLAT9caRf2kWrfWtNX1h21nF/4DRQAqwSSn1jdZ6d6Vj\nWgBvATFa6+NKKWnOcp4zxWX8vDed5clmVuzNoKisYuauu6m57YygNZdHBEoQOKow27hesPEdKD1j\njHUcYYRB+6tdVtbixYt5++23+f7775k8eTLp6emEhoa6rB7RODkSCpuUUvuAz4CvtNZnHHztQcDB\ns030lFKLMDqv7q50zO9sr3kcQGud7nDlDVhOYSk/7E4jMcnMmgOZlJZXtJe4ol2wveFcx9BmLqzS\nAxVkwS9zjNtLS20b/XQaZYRBpOvm6/Pz85k4cSIrV648p4GdBIJwBUd2XuuslLoauBV4Vim1HVik\ntV5Uzbe2xWi3fVYKMPi8Yy4HfJVSKzH2fZ6ttf7o/BdSSs0AZgBERkZWV7JHSj9TzPfJRhD8cjiL\n8krtJQZ1aGW0l4g20bZFExdX6oEKsuCXN+HXeRVh0PkaY51B5Pn/JOvXhx9+yL333ktJSQnt27cn\nISGBHj16uLQm0bg5NFGptV4PrFdKPYMx/78AqC4UHH3//sC1QBPgF6XUBq31OReytdbxQDwYt6TW\nwfu6hZM5RnuJ5UlmNh3LRldqLzGsayhjo0yMiYogvLm0l6iVgkyjL9Gv70KZbY1Gl+uMMLjM9VtR\npqenc+edd6KU4m9/+xv//ve/XV2SEA4tXgvEmPa5FegBLAEcmXg9CVxW6XE721hlKUCW1roAKFBK\nrQauoAHf3XQks8C2RWUqO1Jy7eN+3l4M6xpKTLSJ0T0jaNFU2kvUWn4GrJ9tNKsrs20D2nWMcWtp\nu2pv03a6jz76iN/97neEh4czZ84cJkyY0GDPgIXnceRMIQn4FnhRa72mBq+9CeiqlOqIEQa3YlxD\nqGwJMEcp5QP4YUwvvVaD93B7Wmv2pZ2x71W811xxSaaJrzejuocRE92aUd3CaC7tJS7NmTTjzGDT\ne2CxLdq7PMbY6axtf9fWBhw/fpyxY8eyd+9e1q5dS3x8PA888ICryxLiHI6EQiettbX6w86ltbYo\npR4ClmPckjpfa52slLrP9vxcrfUepVQisBOwYty2mlTT93I3Wmt2ncy1N5w7klnRXqJ5gA/X9Ygg\nJtrE8K5hNPGTVcWX7IzZ2Mtg83yw2PaF7jbOCIM2fV1bm83f//53/vOf/2C1WhkwYAD/+c9/XF2S\nEBd00TYXSqlXtNaPK6UWA785yFU7r7lrmwurVbPl+Gn7GcHJnIr2Eq2a+TGmZwRjo00M6RyKn4+s\nKq4TealGGGx5v1IYjLeFQR/X1lbJwIED2bx5MwEBAcydO5dp06a5uiTRCNVFm4vPbH/KjmsXYSm3\nsvFINglJqSxPTiPjTEV7iYggf8ZGGYvJBnWQ9hJ1Ku8UrH0dtnwA5ba/8+4TjGsGrXu7tLSzrFYr\npaWlBAQEMHnyZIKCgliyZAmBgY18lzrh9hxpiPeQ1npOdWP1xdVnCiWWctYdzCTB1l4ip7DM/ly7\nlk2IjTYRE92avpe1kPYSdS33JKx9DbZ+VBEGPSYZZwamXq6trZJNmzYxYcIEunTpwrp161xdjhBA\n3TbEu4vfni3cfYGxBquw1MKqfRkkJJn5eW86+ZXaS3QOa0asbTFZVJsgWVXsDLkpsOZV2PYxlJcC\nCnpeb4RBhPtsSm+xWJg2bRoLFy4EYNgw1/RNEuJSXDQUlFJTMO4Y6qiU+qrSU82BnAt/V8ORV1zG\nz3vSSUwys3J/OsVlFdfae7YOsjec6xrR3IVVNnA5J2Dtq7D1Y7CWAQqibjTCINy9FnitXLmS66+/\nntzcXFq2bMlXX33FyJEjXV2WEDVW1ZnCr0AWxvqC/1UaPwNsc2ZRrnK6wGgvkZCUyrqDWee0l+hz\nWQvb1JCJ9iHSXsKpTh8zwmDbgoowiJ4Mw2dCeHdXV3dBWVlZ5OXlMW3aNObPn4+Xl1xDEp7poqGg\ntT4CHMHoitpgpecVszzZ2KJy45Fse3sJLwWDO7Yi1tZeonWwtJdwutNHYc0rsH0hWC2gvKDXzTD8\nSQjr5urqfuPLL7/k7bff5scff2Ty5MlkZmbSqlUrV5clxCWpavpoldZ6hFLqNOfekqoArbX22H/9\nJ7ILWZ5s3Dq65fhpe3sJHy/F8MvDiLWtKg4N9HdtoY1F9hFY8zLsWFQRBr2nGGEQ2tXV1f1GXl4e\nEyZMYM2aNec0sJNAEA1BVdNHo2x/NohWjYcy8u1rCHadrNRewseL4V2NILiuRwTBTWVVcb3JOmSc\nGexYBLrcCIMrpsKwJyC0i6uru6B3332Xhx56iJKSEjp16kRiYiJdu7pfcAlRW1VNH52dUL8MOKW1\nLlVKDQV6A58AefVQX61prdlrPmNbVZzK/rR8+3NN/bwZ1d3YtH5Ut3Ca+csGJvUq6xCsfhl2fmYL\nA2/ocxsMexxCOru6uotKT09nxowZeHl58eyzz/KPf/zD1SUJUecc+Wn4NTBQKdUZeB9YCiwEJjiz\nsNrQWrMjJddYTJZk5mhWof25oAAfrutp7FU8rGsoAb7SXqLeZR6E1S/Brs9BW21hcDsMfxxadXJ1\ndRf13nvvMW3aNMLDw3n77beZOHEibdq0cXVZQjiFI6Fg1VqXKaVuBN7UWr+hlHK7u49OZBdy27sb\nOZ5dEQQhzfwYY1tVfFWnEGkv4SoZ+40wSPrCCAMvn4ozg1YdXV3dRR07dowxY8awf/9+Nm7cSHx8\nPPfee6+ryxLCqRzajlMpdTPwe+B625jbTbyvP5TJ8exCWjXzY9IVbYiJNjGwQyu8ZVWx62Tsg1Uv\nQtKXgDbCoO/vYdhj0LKDq6ur0l/+8hdefPFFrFYrgwcPZtas32wvLkSD5OiK5gcwWmcftrXC/tS5\nZdXcaVu7icn92vLX8T1dXE0jl77HCINkWy9FL1/oe7sRBi3cf9+A/v37s3XrVgICApg3bx633367\nq0sSot44sh1nklLqEaCLUqo7xr7Lzzu/tJo5XVgKIJvTuFLablj9IiR/jT0M+v0Bhv4JWlxW7be7\nUuUGdlOmTKFVq1YsWbKEpk2buro0IeqVIzuvDQM+xtgoRwEmpdTvtdZu1ekrp8A4U2gpoVD/0pJh\n1Quwe4nx2NuvIgyC27m2Ngf88ssvxMXF0bVrV9atW8fMmTOZOXOmq8sSwiUcmT56DRintd4NoJTq\ngRESrt/XsJKcorNnCm53uaPhMu8ywmDPt8Zjb3/oPw2GPArBbV1bmwMsFgu33347n31mdImXXkVC\nOBYKfmcDAcC2W5rb/Tp+9pqChEI9SN1hXDPYu9R47O0PA+6EIX+EIM+4VfOnn37ixhtvJC8vzz5V\nNHToUFeXJYTLORIKW5VSczEWrAHchhs2xMuxXVOQ6SMnOrXdODPY953x2CcABtxlhEFzk2trq6G8\nvDzy8/O5++67iY+PlwZ2Qtg4Egr3AY8AZydZ1wBvOq2iWjp7piCh4ASntsHKF2B/gvHYp0mlMIhw\nbW018NlnnzF37lxWrFjBDTfcQFZWFi1atHB1WUK4lSpDQSnVC+gMLNZav1g/JdWc1ppcmT6qeye3\nGGFwYLnx2KcJDLzbCIPAcNfWVgM5OTmMHz+e9evX4+XlZW9gJ4EgxG9V1SX1aYwd1rZitLn4l9Z6\nfr1VVgOFpeWUllsJ8PWS9hV1IWUzrJwFB38wHvs2hYHT4epHIDDMtbXV0DvvvMMjjzxCaWkpnTt3\nZvny5XTu7L79lYRwtarOFG4DemutC5RSYcB3gFuGwmm5nlA3TvxqhMGhn4zHvs1g0D1w9cPQzPOa\n5aanp3P//ffj5eXFc889x1//+ldXlySE26sqFEq01gUAWusMpZTbXonLsU8dSSjUyvENRhgcXmE8\n9guEQTPgqoegWYhra6uF+Ph47rrrLsLDw5k7dy4TJkyQBnZCOKiqUOhUaW9mBXSuvFez1vpGp1ZW\nA/ZQaCLXE2rk2C+wahYcXmk89msOg21h0NTzNow5cuQIY8eO5cCBA2zatIl58+YxY8YMV5clhEep\nKhQmn/d4jjMLuRT26aNmEgoOObrOCIMjq43H/kEw+F648gGPDAOAmTNn8sorr2C1Wrnqqqt46aWX\nXF2SEB6pqk12fqrPQi5FjvQ9csyRNcY6g6NrjMf+wXDlfXDl/dCkpWtruwT9+vVj27ZtNGnShPfe\ne4+pU6e6uiQhPFaD2HKsYo2CnCn8htZGCKx8AY6tNcb8g+GqB2DwfdDEM2/LrNzAburUqYSFhbF4\n8WJpYCfEJWoQoVBxTUHOFOy0hiOrjDA4vt4YCwiGKx80poo8NAwA1q5dy/XXX0/Xrl355ZdfePLJ\nJ3nyySddXZYQDYLDoaCU8tdalzizmNqqmD6SMwW0Nu4iWvkCnNhgjAW0MC4eD55hBIOHslgs3Hrr\nrXz55ZcAjBkzxsUVCdHwONI6exDwHhAMRCqlrgCma60fdnZxjpJ1ChhhcOgnIwxSfjXGmrQ0wmDQ\nDAgIcm19l+iHH35g8uTJnDlzhtDQUL7++muGDBni6rKEaHAcWXvwBjAByALQWu8ARjny4kqpGKXU\nPqXUQaXUU1UcN1ApZVFK3eTI657Pfk2hMd59pDUc+BHevQ4+mWwEQpNWcO0/4dFdMPwJjw8EgMLC\nQgoKCrj33ntJS0uTQBDCSRyZPvLSWh9T6py9jsur+yallDfwP2A0kAJsUkp9U7kNd6XjXgC+d7jq\n8+QWGaEQ3JiuKWgNB34wbi09ucUYaxpitKIYOB38A11bXx349NNPeeedd1i5ciVxcXGcPn2aoCDP\nDzgh3JkjoXDCNoWkbT/AHwb2O/B9gzC27jwMoJRaBMQBu8877mHgS2Cgw1Wfp2L6qBGcKWgN+5cb\nYXDK1sG8aSgMeQQG3N0gwiAnJ4fY2Fg2bNiAl5cXe/bsoUePHhIIQtQDR0LhfowppEggDfjRNlad\ntsCJSo9TgMGVD1BKtQVuwJiOqlUolFt1pTOFBhwKWsO+BGOdQep2Y6xZmNGxdMBd4NfMtfXVkbfe\neotHH32UsrIyunbtyvLly+nYsaOryxKi0ag2FLTW6cCtTnr/14E/a62t501PnUMpNQOYARAZGXnO\nc3lFZWgNzQN88PF22/ZMtac17F1mhIF5pzEWGGGEQf87wa/h3JdvNpt56KGH8Pb25r///S9PPXXR\ny1BCCCdx5O6jeYA+f1xrXV1TmZPAZZUet7ONVTYAWGQLhFBgnFLKorX++rz3igfiAQYMGHBOLTlF\nDXRzHasV9i0z7iZK22WMBZpg6KPQ/w7wbeLS8urSW2+9xYwZMzCZTMTHxzNhwgRMJs/ayU2IhsKR\n6aMfK30dgDHdc+Iix1a2CeiqlOqIEQa3Ar+rfIDW2j4voJT6AFh6fiBUp8FdT7BaYe+3xh7IaUnG\nWPPWMPRP0O8PDSoMDhw4QExMDIcPH2bbtm3MmzeP6dOnu7osIRo1R6aPPqv8WCn1MbDWge+zKKUe\nApYD3sB8rXWyUuo+2/Nza1fyuRpM3yOrFfYsMcIg3XYtvnmbSmEQ4Nr66pDVauWJJ57g9ddfR2vN\nsGHDeOWVV1xdlhCC2rW56Ag4tDGv1vo7jM15Ko9dMAy01nfUohZOF3j4NpzWctj9Nax6CTL2GGNB\nbSvCwMfftfU5Qf/+/dm+fTtNmzbl/fff55ZbbnF1SUIIG0euKZym4pqCF5ANuM0VQI+9pmAth+TF\nxplB5j5jLKgdDHsM+t7e4MLAarVSXFxM06ZNuf3222ndujVfffUVAQEN5wxIiIagylBQxhXgK6i4\nQGzVWv/morMreVzfI2s5JH0Fq1+ETNtyj+BIIwz63AY+HhZuDli9ejU33HADXbt2ZcOGDTz++OM8\n/vjjri5LCHEBVYaC1lorpb7TWkfXV0E15TF9j8otkPQlrH4Jsg4YYy0iYdgTcMXUBhkGpaWl3Hrr\nrSxevBiALl26uLgiIUR1HLmmsF0p1Vdrvc3p1dRCxf7MbnqmUG6BXf9nhEH2IWOsRXujJ9EVU8Hb\nTeu+RMuXL+emm24iPz+fsLAwvv32WwYPHlz9NwohXOqioaCU8tFaW4C+GH2LDgEFGPs1a611v3qq\nsUoVoeBmv2mXW2DnZ7DmZcg+bIy17GiEQe8pDTYMziopKaGwsJD777+fOXPm4OXVABcWCtEAVXWm\n8CvQD5hUT7XUitutUygvgx2LjDA4fdQYa9UJhj8JvW4B7waxr9EFffTRR8ybN481a9YwadIkaWAn\nhAeq6ieUAtBaH6qnWmolp9BN7j4qL4Mdn8LqlyHnmDEW0sUIg+ibGnQYZGdnExMTw6ZNm6SBnRAe\nrqqfVGFKqccu9qTW+lUn1FNjZ+8+CnbVmYKlFHYshDWvQM5xYyykK4yYCdGTwcvbNXXVk9mzZ/Pk\nk09SVlZG9+7dSUxMpH379q4uSwhRS1WFgjcQiO2MwR2VWqwUlJbj46Vo7l/Pv4lbSmH7J7DmVci1\ndf0IvRyGz4ToGxt8GIDRwO5Pf/oT3t7evPzyy3KbqRANQFU/SVO11v+qt0pqofIahaq6rNYpSwls\n+xjWvAZ5KcZYWHdjmijqhkYRBnPmzOG+++7DZDLx3nvvMX78eMLDw11dlhCiDlR7TcGdna7PO4/K\nio0wWPsa5NnW8oX1MKaJel4PjeDumn379hETE8PRo0fZsWMH8+bN484773R1WUKIOlRVKFxbb1XU\nkv1MwZmb65QVw9aPjDA4c8oYC48ywqDHpEYRBlarlT/96U+8+eabaK0ZMWKENLATooG6aChorbPr\ns5DacOqZQlkRbPkQ1r0OZ1KNsYhoGPFn6D6hUYTBWX379mXnzp00a9aMDz/8kMmTJ7u6JCGEk3j0\nfZI5zlijUFYEm983wiA/zRgz9TLCoNv4RhMGVquVwsJCAgMDmTZtGitWrODLL7/Ez8/NFgkKIeqU\nR4fC2TOFls3q4AdVaSFsng/rZkNBujFm6g0jn4Ju46C+LmS7gZ9//pnJkyfTtWtXfv31Vx577DEe\ne+yidycLIRoQjw6FnCLbGoVLuaZQWgCb3oP1b0BBhjHWuo8RBpfHNKowKC0t5eabb+abb74BoGfP\nni6uSAhR3zw7FAouYTVzaQFsehfWvQGFmcZYm35GGHQd06jCAOC7777jlltuoaCggIiICJYuXcqA\nAQNcXZYQop55dCjUuu/RiU3w6RQozDIet+0PI/8CXa5rdGFwlsViobi4mIcffpjXX39dGtgJ0Uh5\ndCjUukPqyv8agdC2P4x8Grpc2yjD4P333+fdd99l3bp1TJo0iZycHAIDA11dlhDChTw7FIpqseta\nYTYcWQXKG373f9AsxEnVua/MzExiYmLYsmXLOQ3sJBCEEB49R3C6Nh1S9yWA1QIdhzXKQHj11Vdp\n3bo1W7ZsoUePHhw5coQePXq4uiwhhJvw2FDQWtduf+bdS4w/e8Y5oSr3ZjabeeKJJwB47bXX2L17\nN5GRkS6uSgjhTjw2FApKyykr1zTx9SbA18EmdMW5cOhnUF7GquRG4vXXX8disWAymXj//fdJTU3l\n0UcfdXVZQgg35LHXFGp1lrAvEaxl0GEYBDb8rp579uwhJiaG48ePs3v3buLj45k2bZqryxJCuDGP\nPVOo1Z1HjWTqyGq18uCDDxIVFcXx48e59tprefVVt9gTSQjh5jz2TKHGaxRKzsDBHwHV4KeO+vTp\nw65duwgMDGTBggVMmuTW22wLIdyIB4dCDe882r8cyksg8ioIau3Eylzj7OKzwMBA7rrrLlatWsVn\nn30mDeyEEDXisdNHuTXdm7kBTx398MMPhIaGMmrUKAAeffRRFi9eLIEghKixBnCm4EAolBbAgR+M\nr3tMdGJV9au4uJibbrqJZcuWARAdHe3iioQQns6DQ+HsNQUHfhs+8ANYiqDdQAhu5+TK6sfSpUuZ\nMmUKhYWFmEwmli1bRr9+/VxdlhDCw3ns9FGN7j7aY7SCpkfDuuBaUlLCo48+ysmTJyUQhBB1wqmh\noJSKUUrtU0odVEo9dYHnb1NK7VRK7VJKrVdKXeHoazu8P3NZkXGRGaCnZ4fCu+++y1VXXQXAhAkT\nyMvL47XXXpOOpkKIOuO06SOllDfwP2A0kAJsUkp9o7XeXemwI8AIrfVppVQsEA8MduT1K3ZdqyYU\nDv0MpfnGxjktO9T0Y7iF9PR0YmJi2LZtG97e3vYGdk2bNnV1aUKIBsaZv2IOAg5qrQ9rrUuBRcA5\nt/5orddrrU/bHm4AHJ7wr1jRXM30kYffdfTiiy/Stm1btm3bRq9evTh+/Lg0sBNCOI0zQ6EtcKLS\n4xTb2MXcDSRc6Aml1Ayl1Gal1OaMDGPLTIfWKVhKjK6o4JGhYDabeeqpp1BK8eabb7Jz507atGnj\n6rKEEA2YW0xGK6VGYYTCny/0vNY6Xms9QGs9ICwsjHKrJq/YCIWggCpmwA6vhJI8iOgFIZ3rvnAn\neeWVVygtLcVkMvHRRx9hNpt56KGHXF2WEKIRcOYtqSeByyo9bmcbO4dSqjfwLhCrtc5y5IXzisrQ\n2ggEH+8qcs3Dpo6SkpKIjY0lJSWFvXv3Mm/ePG6//XZXlyWEaESceaawCeiqlOqolPIDbgW+qXyA\nUioS+Ar4vdZ6v6MvbF+j0KyqqaNS2LvU+NrNQ8FqtXLffffRu3dvUlJSGD16NLNnz3Z1WUKIRshp\nZwpaa4tS6iFgOeANzNdaJyul7rM9Pxf4BxACvKWMPZItWusB1b32aUfWKBxdbeyfENYDwi6/xE/j\nXL179yY5OZnAwEA+/fRTJkxo2A37hBDuy6krmrXW3wHfnTc2t9LX04HpNX3d3CIH1ii4+dSRxWKh\nsLCQoKAg7rnnHtasWcPChQulX5EQwqXc4kJzTZ0uqKbvUbkF9rjv1FFCQgIhISFcc801APzxj3/k\niy++kEAQQricR/Y+Ol3dGoVja6EoG0K6Qrj73NNfWFjIjTfeyPLly1FK0bdvX1eXJIQQ5/DIUMip\nbo1C5akj41qFyy1ZsoSpU6dSVFREmzZtSEhIoHfv3q4uSwghzuGR00c5RVXsz2wthz3fGl+70dSR\nr68vpaWlPPHEE5w8eVICQQjhljzyTKHi7qMLhMLxX6AgA1p2BFOveq7sXO+88w7z589n48aNjBs3\njvz8fAICAlxakxBCVMUjQyGnqr0U3GDqyGw2M3bsWHbu3Im3tzf79u2jW7duEghCCLfnkdNHFXcf\nnRcKVivstq2Pc9HU0X//+1/atWvHzp077YvRunXr5pJahBCipjwyFHKLLjJ9lPIr5JshOBLa1P+d\nPWazmb/+9a94e3vz1ltvsWPHDkwmU73XIYQQteWRoVBxS+p5oWCfOppUr1NHs2bNsjewW7BgAWlp\nadx///319v5CCFFXPO6agtZQWFqOj5ci0L9S+VZrpVC4vl5q2b59O+PHj+fUqVMcPnyY+Ph4pk6d\nWi/vLYQQzuBxZwoWqwaMhWuq8tnAqa2QdxKC2kLb/k6twWq1Mn36dPr168epU6eIiYnhjTfecOp7\nCiFEffC4M4VyeyicP3X0tfFnj0ng5D2Lo6Oj2bNnD0FBQSxatIjY2Finvp8QQtQXDwwFK3Be3yOt\nz72e4ASVG9jdf//9rFu3jk8++QQfH4/7KxRCiIvyuOmj8krTR3ap2yHnOARGwGWD6/w9ly5dSqtW\nrewN7B5++GEWLVokgSCEaHA87qfa2WsK55wpnF2b0GMieHnX2XsVFhZy/fXX88MPP6CUYuDAgXX2\n2kII4Y48LhTKrRpFpTMFrSuuJ9ThgrXKDezatWtHQkIC0dHRdfb6Qgjhjjx4+sh2ppCWDNmHoWko\nRF5dZ+/j5+dHWVkZM2fO5MSJExIIQohGwePOFCxWjQ+VWlycvcDcYwJ4X9rHmTNnDh988AGbN28m\nNjaWM2fOSL8iIUSj4nGhUH7+NYU62Hbz1KlTjB07lqSkJHx8fKSBnRCi0fLY6aPgJn6Qvhcy90GT\nltBhWK1e71//+heRkZEkJSXRt29fTp48KQ3shBCNlseFguXsOoVmvhVnCd3Hg/dF9muuwqlTp3jm\nmWfw8fFh3rx5bN26lfDw8LosVwghPIrHhULF9JFfrXodWa1WnnvuOUpLS2nTpg2LFi0iPT2d6dOn\nO3LdCw8AAAmkSURBVKNcIYTwKB57TaFF4VFITwb/YOg4wqHv3b59O+PGjSM1NZXjx48THx/PLbfc\n4sRqhRDCs3jcmYIGmvh6479/qTHQfRz4XGAHtkqsVit33nknffv2JTU1lXHjxkkDOyGEuACPO1MA\n251HNbjrKCoqir179xIcHMz//d//MXr0aCdXKIQQnskjQ6G7fxaYd4Jfc+g06oLHlJaWUlhYSIsW\nLXjwwQdZv349H330kfQrEkKIKnjc9BHAaLXB+KJbDPj+di3BkiVLaNWqFddeey0ADz30EAsXLpRA\nEEKIanjkT8mritcZX5w3dZSfn09cXBw///wzSimuvrru2l4IIURj4HGh4IuFDiV7wbcZdLnOPv7l\nl19y++23U1xcTGRkJImJifTo0cOFlQohhOfxuOmjYAqMLy4fA75N7ONNmzbFYrHw9NNPc+zYMQkE\nIYSoBaeGglIqRim1Tyl1UCn11AWeV0qpN2zP71RK9avuNYOVLRR6xjF79mwGDBgAQGxsLAUFBTz/\n/PN1/CmEEKLxcNr0kVLKG/gfMBpIATYppb7RWu+udFgs0NX232DgbdufF9WUYrJLWzLylqfZtXvv\nOQ3s/PyqXq8ghBCias48UxgEHNRaH9ZalwKLgPMXFcQBH2nDBqCFUqp1VS+aW6LpNjubXbv30r9/\nf1JTU6WBnRBC1BFnhkJb4ESlxym2sZoec46jORqtfHj33XfZvHkzoaGhdVKsEEIID7n7SCk1A5hh\ne1iSVVCWNH369MbUxC4UyHR1EfVMPnPjIJ+5/rR35CBnhsJJ4LJKj9vZxmp6DFrreCAeQCm1WWs9\noG5LdW/ymRsH+cyNg7t/ZmdOH20CuiqlOiql/IBbgW/OO+Yb4A+2u5CuBHK11qlOrEkIIUQVnHam\noLW2KKUeApYD3sB8rXWyUuo+2/Nzge+AccBBoBC401n1CCGEqJ5Trylorb/D+MFfeWxupa818GAN\nXza+DkrzNPKZGwf5zI2DW39mZfxcFkIIITywzYUQQgjncdtQcEaLDHfnwGe+zfZZdyml1iulrnBF\nnXWpus9c6biBSimLUuqm+qyvrjnyeZVSI5VS25VSyUqpVfVdY11z4N91sFLqW6XUDttn9vhri0qp\n+UqpdKVU0kWed9+fX1prt/sP48L0IaAT4AfsAHqed8w4IAFQwJXARlfXXQ+f+Wqgpe3r2MbwmSsd\n9zPG9ambXF23k/83bgHsBiJtj8NdXXc9fOangRdsX4cB2YCfq2u/xM89HOgHJF3kebf9+eWuZwpO\naZHh5qr9zP/f3r2HWFVFcRz//kpNU7NUih7UmJaaNUpPSSFNe2gYFqKU2YPo/bLIJCyjxx+CBWVi\nDyzGP1JBswQRScNXOqZj6hjaU0WkyDArGcY/nFn9sffcrsPM3DPDzJ1zvesDF7xnzjl77XOdve7Z\nd+7aZrbZzI7Gp1sI3+soZEleZ4BngM+Bw/kMrg0k6e+9wDIzOwhgZsXQZwO6SxLQjZAUTuQ3zNZl\nZhsI/WhMasevtCaFNimRkXLN7c/DhHcahSxnnyVdCNxFKJZY6JK8xpcD50haJ2m7pPvzFl3bSNLn\nucBA4DdgN/CcmdXmJ7x2k9rxqyDKXLiTSRpJSArD2zuWPHgXmG5mteGN5CmvA3ANMAroApRL2mJm\nP7VvWG3qNmAncDPQF1gtaaOZ/du+YRWntCaFViuRUUAS9UdSKTAfGGNmR/IUW1tJ0udrgcUxIfQG\nxko6YWZf5ifEVpWkv4eAI2ZWBVRJ2gAMBgo1KSTp80PALAuT7b9I2g8MALbmJ8R2kdrxK63TR8VY\nIiNnnyVdDCwDppwi7xxz9tnM+phZiZmVAEuBJws0IUCy/9fLgeGSOkg6k7C+yN48x9makvT5IOHO\nCEnnAf2BfXmNMv9SO36l8k7BirBERsI+zwR6AfPiO+cTluLCWrkk7PMpI0l/zWyvpFVAJVALzDez\nBv+ssRAkfI3fBMok7Sb8Nc50MyvoyqmSFgEjgN6SDgGvAR0h/eOXf6PZOedcRlqnj5xzzrUDTwrO\nOecyPCk455zL8KTgnHMuw5OCc865DE8KLnUk1cQqoXWPkib2LWmsEmUz21wXK3nukrRJUv8WnGO8\npCuynr8haXSOY1ZKOruFcW6TNCTBMVPjdx6cy8mTgkujajMbkvU4kKd2J5vZYGABMLsFx48HMknB\nzGaa2ZqmDjCzsWb2dzPbqYtzHsninAp4UnCJeFJwBSHeEWyU9F183NjAPoMkbY13F5WSLovb78va\n/pGk03M0twHoF48dJWmHwhoWn0o6I26fJWlPbOftGM+dwOzYTl9JZZImKKwnsCQrzhGSVsR/H5DU\nu4VxlpNVRE3SB5IqFNYkeD1uexa4AFgraW3cdquk8ngdl0jqlqMdV0Q8Kbg06pI1dfRF3HYYuMXM\nrgYmAXMaOO5x4D0zG0KomXRI0sC4/7C4vQaYnKP9ccBuSZ2BMmCSmV1FqADwhKRehMqtg8ysFHjL\nzDYTShdMi3c3v2adbw1wg6Su8fkkQgnpjBbGeTuQXfJjRvyGeylwk6RSM5tDqD460sxGxgT0CjA6\nXssK4IUc7bgiksoyF67oVceBMVtHYG6cQ68hlJiurxyYIekiwpoEP0saRag6ui2WBulC4+syfCap\nGjhAWMOhP7A/q87UAuApQqnn48An8R3/iqY6E0s9rALGSVoK3AG8VG+35sbZibD2QPZ1mijpUcLv\n9fmEqazKescOjds3xXY6Ea6bc4AnBVc4ngf+IFQMPY0wKJ/EzBZK+pYw6K6U9Bihls4CM3s5QRuT\nzayi7omkng3tFAf56wkD+QTgaULZ56Ysjvv9BVSY2bF6P29WnMB2wucJ7wN3S+oDvAhcZ2ZHJZUB\nnRs4VsBqM7snQTuuCPn0kSsUPYDf4+IrUwjF1U4i6VJgX5wyWU6YRvkamCDp3LhPT0mXJGzzR6BE\nUr/4fAqwPs7B9zCzlYRkVbdW9jGgeyPnWk9YnvER6k0dRc2KM5aZfhUYKmkAcBZQBfyjUGl0TNbu\n2XFtAYbV9UlSV0kN3XW5IuVJwRWKecADknYRau1XNbDPROB7STuBKwnLHe4hzKF/JakSWE2YWsnJ\nzI4TqlcuiRU8a4EPCQPsini+b/h/Tn4xMC1+MN233rlqCNNMY2hguqklcZpZNfAO4XOMXcAO4Adg\nIbApa9ePgVWS1prZn8CDwKLYTjnhejoHeJVU55xzWfxOwTnnXIYnBeeccxmeFJxzzmV4UnDOOZfh\nScE551yGJwXnnHMZnhScc85leFJwzjmX8R9KpbFEzGwK8AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3feec6f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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UW3670oLino7NmBrclqD2xVpQFKpG1cdl6devHzt27KBOnTp88sknTJ061dEh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\nwUHBzMwKDgpmZlb4G+hv9zHxkPp8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3feff1fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pJTOPZbtjWbrzPMmZxniBl4crf+zXkol9/GnscUMF0owE2DkXohZBgbHfAf79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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3feee1518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0gftrEXkPSPPgcw4RGQEsByKBGcaYHSIyzPX+lPKVHOIcObBlDqx5FY6GZhg4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\n/wPQDQAkES0S8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fee1a588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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0KSmJJ598kpCQEF5//XX+8pe/OB1JqYCXXVG4YIxJATDGHBcRvROX3yTttsVg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c3fedc6978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "draw_roc(y_train,y_train_pt,'pt_train')\n",
    "draw_roc(y_test,y_test_pt,'pt_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_lr,'lr_train')\n",
    "draw_roc(y_test,y_test_lr,'lr_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_svm,'svm_train')\n",
    "draw_roc(y_test,y_test_svm,'svm_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_dt,'dt_train')\n",
    "draw_roc(y_test,y_test_dt,'dt_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_gnb,'gnb_train')\n",
    "draw_roc(y_test,y_test_gnb,'gnb_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_rf,'rf_train')\n",
    "draw_roc(y_test,y_test_rf,'rf_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_gbdt,'gbdt_train')\n",
    "draw_roc(y_test,y_test_gbdt,'gbdt_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_bg,'bg_train')\n",
    "draw_roc(y_test,y_test_bg,'bg_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_ab,'ab_train')\n",
    "draw_roc(y_test,y_test_ab,'ab_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_xgb,'xgb_train')\n",
    "draw_roc(y_test,y_test_xgb,'xgb_test')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "draw_roc(y_train,y_train_lgbm,'lgbm_train')\n",
    "draw_roc(y_test,y_test_lgbm,'lgbm_test')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
